| Source: Stuart C. Dodd Institute for Social Innovation http://www.stuartcdoddinstitute.org/mathematical-sociology.shtml Papers First Draft April 6-8, 2003 Table of Contents: Author's Preface Author's Preface The "Road to Relativity Theory" was an interesting one. Albert Einstein has given credit to the mathematician Riemann whose non-Euclidian mathematics was one of those instruments of thought with which Einstein was able to work in order to develop the experimental physics and cosmology of relativity theory. This is an example of the study of mathematical lineages in history of science, in this case the history of physical and astronomical sciences. In the study of social sciences, the scholarly analysis of mathematical lineages is certainly a minority pursuit, but I would suggest a very fruitful area for research in the study of those instruments of thought most suited to scientific innovation for social policy and political creativity. I would like to suggest that in the study of mathematical sociology and social mathematics Stuart C. Dodd, although he is a minor player in the official histories of sociology, can be for us a guide to the evolution of mathematical sociology in those directions most suited to innovation in the fundamentals of social-scientific thinking. We will in this monograph, therefore be looking at the mathematical ideas of sociologist Stuart C. Dodd (1900-1975). We will be looking at the thinking of Richard J. Spady (b. 1924) and the way in which Spady has introduced to the world the idea of Social Quantum Mechanics. We will explore the hypothesis that this social quantum theory will bear an abundant harvest in social policy and social change and social innovation, in the same way the quantum theory has led to so many fruitful inventions deriving from our understanding of the so-called subatomic world. In other words, to cite a favorite aphorism of Richard J. Spady, we are looking at a Golden Age for scientific sociology and the prospect of an imminent breakthrough in social science research and its applications. The intellectual community of the heirs in social thought of Stuart C. Dodd is a small but potent one, extending from coast to coast in the USA and to other continents in its outreach. From a number of different directions the Dodd scholars can be seen to be converging on the theme of social quantum theory, even if it is known by another name. For example, Dr. Kenneth Miller, MD, has invented the Vibrational Relativity Theory (see http://www.vibrationalrelativity.org). According to the well known aphorism that Ontogenesis recapitulates phylogenesis (ref. Ernest Haeckel, The Riddle of the Universe early 20th Century) the social sciences can be seen to be reproducing in their own history the intellectual history of the physical sciences in their movement from classical physics to relativity theory to quantum theory to super-string theory and beyond. The fact that relativity theory has been described as the last outpost of classical physics does not invalidate this point. We can put the same issues from a different angle by saying that our purpose in this community of deutero-Doddites is to re-imagine the core definition of social science taking into account all the revelations about absolute reality which the quantum world of thought gives to us (ref. Margaret J. Wheatley, Leadership and the New Science). In intellectual history the reinvention of science, by whatever name, is a repeated motif. For example in the 17th Century, the realm of natural philosophy in the era of mutant was a way in which science began to overthrow dogma and experimental method began to replace superstition. In the intellectual turmoil of the era of Einstein's early years at the beginning of the 20th Century there was a distinct sense that not only physics but science was being reinvented. And to a degree, this perception was accurate. To suggest, as we are doing here, that social science may do likewise a hundred years later is NOT merely to assert that social science rides on the coattails (long way behind) of the so-called physical and mathematical sciences. We offer a far more intriguing hypothesis. If, as is increasingly seen in such fields of study as ontology, personology, and theology, the Personal is seen as having a greater degree of epistemological ultimacy than the impersonal, then it would follow that a fundamental revolution of thought within the social sciences, or to be more exact the socio-politico-ethical sciences, would imply a breakthrough in all of science, as it would then be seen that the Cosmo-human parameters of all thought of science would be an expression of, or a journey towards, the deepest imaginable reality relevant to the human condition. And this is all that we need to know in the most literal sense. For there is an ancient tradition going back at least on the Western side to the Greek philosopher, Protagoras, the teacher of Socrates, that "man is measure of all things." What this means for us is something along the lines of the idea that what concerns the human condition is the proper study of human kind, what doesn't concern it has no existence. Or as Ludwig Wittgenstein (d. 1953) said in another context "wovon Mann nicht sprechen kann, darusser muss es schweigen "- translation: "what we cannot speak about, we had better pass over in silence." This is not a trivial point. It has to do with the moral basis of scientific inquiry. There is a sense we have learned from existential philosophers such as Kierkegaard, that the present moment and its imminent concerns for the human condition for those whom we love and for ourselves, are the things that matter. The rest in the sense of existential psychology and philosophy have no meaning, no existence, and no place in our lives and, particularly, no place in our hearts. This raises the intriguing question of what a heart-centered sociology might look like. And, this in turn could be translated into the question of what would be sociology of maximum ethicality, if we can put it this way. Quantum Thought offers a way out of the apparent riddle in which we are faced with a choice of value free sociology on one hand and ideologically driven social policy making on the other hand. The Sociology of the Heart bypasses this paradox or resolves this dichotomy in a harmonious lynch pin of thought. It offers us an immediacy of perception of the human social condition and some of the tools with which to deal with our most pressing concerns. For example, the concept of immediacy is both physical and social. It has to do with social time, which is one of the most fruitful fields for applying social quantum thought. The latter gives us confidence in looking at our capacity as socio-political beings to act in the now, with immediacy and, if necessary, for something which can only be called instantaneous action, or if this is not too paradoxical, even more speedily. Social quantum thinking collapses many of the distinctions between physical and personal time and gives us new powers to act resourcefully for social higher purposes. Signed, Richard S. Kirby, PhD Chapter 1 - Science and Sociology: The Legacy of Stuart C. Dodd There is a sense in which we are at the dawn of Stuart C. Dodd's scholarship. This seems to be a pattern in the lives, or after lives, of great thinkers. Stuart Carter Dodd was born in 1900 and died in 1975, but it wasn't until 20 years after his death that the systematic study of his work began. If I may be allowed an anecdote from my own history as a scholar, we have a comparable case in the life of W. Olaf Stapledon (1886 - 1950), it was not until 1975, the same 25 years period after the death of Stapledon, that I was able to join the other Stapledon scholars in the actual home and writing places of the late "cosmic philosopher" to give him the epithet assigned to him by science fiction historian, Sam Moskowitz. So, although the systematic scholarly analysis of the legacy of Stuart C. Dodd is a few years old there is a sense in which we are still are at its beginning. This is especially true in the sense that this monograph is the first expression to a non-Dodd audience of the fruits of the first (approximately) ten years of the systematic Dodd scholarship. We can mark this transition by saying that it is when we reached out to a wider audience than the small circle of Dodd scholars, that we can begin to realize that our laboring in his vineyard has indeed begun to bear fruit. Accordingly, we shall now enter the thought world of Stuart C. Dodd in terms of mathematical sociology by a close study of some of the key ideas of his major text in the field. This text is called "Dimensions of Society" and was published by the MacMillan Company during the years of the 2nd World War. In fact, it first appeared in 1942. At that time, Stuart C. Dodd was chairman of the Dept. of Sociology at the American University of Beirut. Actually, there is an Arabic text used as a kind of frontispiece by the author. Stuart Dodd also chose to put opposite the title page of the book a page, which has on both sides a summary of his argument. The first page gives a summary of formulae of S-Theory. Here we can see the general approach to mathematical sociology, which the author is pursuing. The first heading under S-Theory is General Formula: (the author wrote) The generalization, "People's characteristics and environments change," can be more rigorously stated as: "Any quantitatively recorded societal situation (S) can be expressed as a combination of: 4 indices ((I)), namely: of time [T], space [L], a human population [P], and indicators [I] of their characteristics; each modified by 4 scripts, namely: the exponent [I ], and descripts denoting a S = (T;I;L;P) series of classes [I ], of class-intervals [ I], and of cases [ I]; all combined by 8 operators (;), i.e.: for adding [+], subtracting [-], multiplying [x], dividing [/], aggregating [:], cross-classifying [::], correlating [.], and identifying [']." The S-theory is a system of hypotheses which assert that combinations of these basic concepts [in square brackets] will describe and classify every tabulation, graph, map, formula, prose. I would like to draw particular attention to the final sentence of this opening statement, namely, that "The S-theory is a system of hypotheses which assert that combinations of these basic concepts [in square brackets] will describe and classify every tabulation, graph, map, formula, prose paragraph, or other set of quantitative data in any of the social sciences." We can see here that the goal of the author is encyclopedic, if not absolutist. His desire which is expressed in his other work "Possible Acts of Men" is to find a formula for human actions, or acts, so that in principle one would be able to describe the set of all deeds of humanity. We should also take into account the graphic representation of the Dodd Theory. This appears under the heading "The Quantic Solid" of S-Theory, a diagram of the Quantic Classification of Societal Phenomena. Dr. Dodd portrays the four sectors of Societal Situations. Each block in the diagram represents one class of quantitatively expressed societal situations. A "Quantic" number identifying each block is composed of the exponents on the four indices in the Quantic formula: S = T I L P We can see the influence of Set Theory [associated with George Cantor (1854 - 1918)] in the representation by the author of his theory of social phenomena. Let us be more exact and use the method of the Classicist to try and ascertain the purpose of the author. The purpose of the author is initially what is implied in the phrase "Quantic classification of societal phenomena," namely to provide a conceptual and methodological apparatus for measuring by Quantification and Classification those phenomena which occur in society and which constitute the life and time of a society. The author is concerned also to look at societal situations. The classification of situations is a very interesting subject and one in which we can compare the social approach of Stuart C. Dodd with the psychological approach of Frederickson (b. 1970) who was concerned with a taxonomy of situations. This is perhaps a suitable time point in our exposition to observe that our present task is not primarily to judge or assess or even to employee the S-Theory of Stuart C. Dodd, but to comprehend it. This is the urgent task of the Dodd scholar: to enter his thought world as penetratingly as we can and from that "inscape" [this term is to be credited to Gerard Manley Hopkins, the Jesuit poet, (1844 - 1888) ]. One way we can approach the scholarly study of Stuart C. Dodd's Mathematical Sociology is to see it as existing in embedded layers. Thus the study of Dimensions of Society is a way of expressing the goal of a Quantitative Systematic Social Science, or sociology, the purpose of which is stated by the author on page 3, P1 to be, "to begin constructing a quantitative systematic science of sociology" -Dimensions of Society (DOS), page 3. This highest embedding layer of mathematical, or quantitative, sociology contains within itself the particular exposition of the theory of the DOS, and within this is the embedded layer of the S-theory and within the theory we have the ingredients of the theory. It's also helpful at this point if we can restate in contemporary terms what the author's purposes might be. I would suggest as a first attempt in this direction that Dr. Dodd was endeavoring to provide both a philosophy of mathematical sociology and a mathematical technology of mathematical sociology. Collectively we could restate this as mathematical social science, or less accurately, I think, social mathematical science. Such definitions and attempted elucidations are of little value unless they can have some demonstrable or at least hypothetical value of their own. I would suggest that the value of mathematical social science or mathematical sociology over against sociology in general is to be found in a function well encapsulated by Jerome S. Bruner is his famous 1966 empirical study with co-authors Goodnow and Austin, Studies in Cognitive Growth (1966), where Bruner, et al, spoke of the "amplifiers of human ratiocinative capacity." Such amplifiers include symbolic representation and the whole realm of mathematical thinking, including algebra, geometry, arithmetic, calculus, set-theory and so on. There is a sense in which the particular success, or even coherence, of Dr. Dodd's effort providing a philosophy of mathematical sociology and it's attendant mathematical technology is neither here nor there. This is the case of the free play of the intellect in which it's almost as important to play the game as to win, or to put it in slightly more academic terms, it is as valuable to essay or attempt a paradigm construction of this kind as it is to produce an empirical model which is resoundingly successful. In this respect, Dr. Dodd has functioned as a pioneer, as a kind of intellectual hero or wagon scout making his foray into uncharted territories of the mind in order to provide social scientists with a greater intellectual power to do that which they have to do in relation to society. I deliberately refrain from phrases such as "doing social science" or "studying society" because I regard those as begging the question as to the tasks of a Mathematical Sociology. Dr. Dodd was writing 60 years ago, and since then not only Modernism, but Post-Modernism have given us a very different perspective on the tasks of a "social science," a fortiori or political science. In addition, the assimilation to the public mind of the existential philosophies of Europe and Scandinavia through such authors as Heidegger, Sartre, Kirkegaard, and Colin Wilson in England, have made it almost impossible to de-existentialize without a real sense of the loss of humanity within the sociological task. Here at the Stuart C. Dodd Institute for Social Innovation over the last seven years we have in various settings and in various ways endeavored to lay the foundations of spiritual sociology, not in the abstract sense, but to conceive one of boundless compassion, one of absolute idealism, one in which the idealism is not set in contrast to practicality or realism but is in fact the highest expression of practicality and realism. In fact, our working hypothesis at the Institute has been: the Ideal is the Real: this is my personal summary in a phrase of the Platonic Philosophy. It is also a good thumbnail encapsulation of the Perennial Philosophy as laid out for us in such books as Aldous Huxley's' "Eponymous Treatise: The Perennial Philosophy." Thus we Post-Moderns no longer occupy a world of thought in which it is open to us to construct large, impersonal, abstract conceptions of society. The harrowing experiences of two World Wars, the encounters with radical evil of the 20th Century left us somewhat shaken in our attempts to see our tasks as defining the rationality of society and so on. Furthermore, there's a sense in which large system building has fallen into intellectual disrepute, and has been replaced not just by empiricism and it's attendant experimental philosophies of social investigation, but also by a more subtle piecemeal approach to policy making and practice as implied in the philosophy of science of such authors as Sir Karl Popper in his books The Open Society and It's Enemies, The Logic of Scientific Inquiry, Conjectures and Refutations, and so on. From our point of view, this means that our approach to social theory making and model building has to exist in a kind of quantum-electron double-headed coin in which the improvement of society and the description of society are two facets of some mysterious higher or larger reality. Social quantum thought, as introduced to the world by Richard J. Spady, thus presents itself as a successor or paradigm to the S-theory of Stuart C. Dodd. Whereas the goals of S-theory were to provide apparatus conceptually for the description of the dimensions of society, social quantum theory has purposes much more subtle and impossible fully to describe. This latter sentence would be the way in which Heisenberg's famous quote "Uncertainty Principle" impinges on social thought. Since the act of observation changes that which it observes in the quantum world, we cannot aim at a complete description of society. In this respect, quantum thought categorically refutes the over arching hypotheses of Stuart C. Dodd that there can be a Set of all Social Acts. Furthermore, one of the distinct weaknesses of S-theory is its more of less complete omissions of ideals as forms of energies. Indeed the topical index of DOS2, beginning on page 931, has no space for ideals, nor do we see any presence of the Arts considered as a whole although the author does give one reference to esthetic indicators as indicated on page 257. Furthermore, the major elements of S-theory do not include social energies although societal energy is mentioned on page 827. At this point, we should say that Stuart C. Dodd's attempt at the mathematization of social thinking to the eyes of scholars sixty years later has a distinct flavor of positivism and scientism. (The authors cited by Dr. Dodd do not include either Socrates or Plato, and Aristotle is only mentioned on one page.) Our task as scholars is certainly not to find fault with the remarkable edifice of thought which is the pioneering of Dimensions of Society. Instead, I prefer to see it as something like a telescope which enables us to see vistas of our own potential thought which otherwise we would not have considered. In this case the vista that opens up before us is that of a mathematically articulate social quantum theory. Richard J. Spady designated the first iteration of this as Social Quantum Mechanics, or SQM. But in the spirit of Dimensions of Society we can venture to investigate the larger and more fruitful field of social quantum science in general and as it were a still larger environing area of thought which we should designate at social quantum theory. It probably does no harm to employ the term quantum social theory and quantum social science, but the Law of the Jungle in the Marketplace of Ideas will determine which of these or some other will predominate in the general field of social quantum discourse. To put this more formally, Dr. Dodd's mathematical sociology is a positive stimulus and inspiration to the architects of social quantum theory and it's attendant fields such as Vibrational Relativity Theory. This is all the more reason, perhaps, why we should be so thoroughgoing in our appraisal of the conceptual and paradigmatic completeness and accuracy of Dr. Dodd's pioneering effort. Last, we can observe that his realm of thought does not explicitly take note either of relativity theory nor quantum mechanics; neither is Einstein even mentioned in the Index. In a way, this makes things even easier for the deutero-Doddites because the field of social quantum thought is more or less virgin territory, terra incognita. However, although the territory may be unexplored, our movement towards it is one in which we stand on the shoulders of Giants - as Sir Isaac Newton said of his predecessors. One of the features of social quantum thought and its effortless, intrinsic harmony of theory and practice, practical in ideal and so on, is that it enables us to oscillate as in the famous double-slit experiment of elementary quantum theory between case studies (real or imagined) and theory building. With this in mind, let us turn our attention to a social quantum approach to education, school construction, curriculum development, and the like. The social quantum approach to education offers many advantages which were previously unavailable until this particular realm of thought was opened up by Richard J. Spady and colleagues. For example, we are not bound by static or linear conceptions of social time but can ask the following kind of question: If we could freeze-frame and ideal educational moment, what would be happening? As a working teacher at the University of Washington, I developed, with my students, the following definition of the ideally profitable moment, or instant, in the classroom: is one in which all of the members in the classroom on that occasion are contributing all of the energies and their ideals to the task at hand. This is a formal theoretical statement and an empirical one, too. It can be tested very easily by asking how many of the students are awake. If some are asleep, that instant is not an ideally profitable one for the classroom. Here is another example of applied social quantum thought in the educational field, according to the basic postulate of social quantum mechanics, as developed by Richard J. Spady, a person can be both an individual and a social unit; that is to say, an individual and a citizen (The extent to which this theory is refuted by the "looking glass self" theory of Charles Cooley is something that we must defer at present to a research student). But let us use this quantum self-theory of personhood, or social personhood, or social identity in the classroom and try some ideas that are well known but not easily stated except in the brevity of social quantum thought. What I have in mind is to say that a student in the classroom is both the teacher and the student. This is a simple axiom, which has profound consequences. Granted, it is a cliche for teachers, but it is a cliche whose content is more honored in the breach than in the observance. For if the teacher, at the beginning of the semester, is to tell the under-graduates that they are teachers just as much as the teacher is a teacher and the student is a student, just as much as the students are students, then a very different concept of the classroom would ensue. And this is one of the derivatives of the social quantum theory, which I am developing under the paradigmatic name of EITP, Educational Innovation in Theory and Practice. Let us take another application of social quantum thought, this time to the highly topical subject of the Military. The Armed Forces are of necessity teachers of great ethical principles, such as the principle of self-sacrifice, the principle of courage, the principle of character development, the principle of community identity, the principle of loyalty, and so on. Nearly all of these, if not all of them, are virtues which Aristotle, and other political scientists, would recognize as the virtues of the ideal citizen. Therefore, it's well known that the Military is a training ground for moral character and, therefore, for civic service. But we can re-state this in social quantum terms, if we wish in symbolic logic and set theory, as the principle that there is a political property "x" such that "x" is expressed in the alternating double identity of the soldier and the citizen. The social quantum political scientist is asking the question, then, what is "x"? "X" is a political unit, "x" is an ideal citizen, "x" is a civic transcendental in human form. Practically speaking, this social quantum theory has profound and immediate implications for Army recruitment and also for the work of Military Chaplains in the Veteran's Administration. For one the one hand the Army can present itself more and more as a training ground for citizenship and ideal citizenship. And, conversely, the task of civics educators in many, many educational and political settings may be to display the potential of both soldier and citizen to advance the level of civilization in both the Armed Forces and the realm of Mufti (out of uniform). In other words, social quantum thought in relation to the Armed Forces, the Military Chaplaincy, and so on, represents an approach to the leadership of civilization building within the development of both the Military and the citizens of tomorrow. Let us raise the stakes of our conversation, in every sense of the word, by turning our attention to the contribution of Mathematical Sociology (past, present and future) to the worlds of money and the civilization building in the world of money. There is a natural and almost inevitable affinity between monetary economics and banking and mathematical sociology. There are few arenas of life in which social mathematics figure more prominently than in the worlds of debt, credit, banking, wealth creating, financial journalism and the like. If, therefore, we postulate the emerging field of social quantum finance, or SQF, we would immediately have some fresh approaches to the definition of profit, of money, of monetary consumption, or world national product and the like. Building on our notion of the soldier citizen, as social counterparts of the electron in its modes as wave and particle, we can also think of the ideal citizen as an ideal participant in the worlds of social money. This is a quite fresh approach to the world of banking, monetary economics, taxation, fiscal policy and the like. For it offers us a picture of the citizen-banker, or citizen-wealth-creator, or money-making-citizen, which transcends quite thoroughly the somewhat static notions of the debtor, creditor and the like. Instead, according to social quantum theory and its political science manifestations, we can dare to see every civic or political person (i.e., a citizen) as a wealth creator of potentially unlimited scope. In fact, by definition, in this theory, in this model, each citizen would be the bearer of an absolute ideal and potential for the raising of social wealth to an infinite level. In my article, "Infinite Profit at Infinite Speed," co-authored with Karun Philip last year, I pointed out that there are technical philosophical reasons why "Infinite Profit at Infinite Speed" or to put it another way, perfect wealth now, is becoming a new horizon of financial ideality and idealism. This completes our first foray into the thought world of Stuart C. Dodd and its applications to the present day. What I've described could be placed under the heading of First Concerns of the Deutero-Doddite Community. And, this being the case, it behooves me now to rest my case and hear the verdict of that jury known as my peers. Thank you for your attention. |
